TLDR: it's harder to have more kids when the law demands we keep them safe to a certain standard when children ride in cars. Car seats take up more space than children. This is a financial pressure against larger families.

If your problem is low birth rates in America, sure, car seat laws are a small but measurable and possibly easily-remedied contributor to said problem. But really that's one of like a thousand things[0] including car culture generally. Trains, light rail, and busses don't add that pressure, and bikes are cheap.

[0] TFA mentions a bunch of other pressures, but that list is certainly non-exhaustive, and seems very facile, tbh.